WEBVTT
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this question chooses a table. Um, that describes
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how maney days reached 90 degrees in New York's Central
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Park. Um, first, it wants us to
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make a frequency table group thes by bins of length
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five, starting with 04 So we'll have 045 to
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9 10 to 14 and want six of them.
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So we'll go up to 15 to 1922 24 and
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finally 25 to 29. Now, the way I'm
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gonna do is I'm gonna go through and for each
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one, I'll just make a little mark. Um
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, by the been, that number falls in.
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So we start 11 8 11 38 So to do
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that, I will make a mark where 11 goes
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here 10 to 14 that mark where it goes 11
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8 11 than three and then eight. And I'll
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keep doing that. I've actually already done it.
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And I'll find that the frequencies we have our nine
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in the first been nine in the second, 14
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15 and one. So these are our frequencies.
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Um, now wants me to make a hist a
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gram and a okay, frequency polygon. So I'm
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gonna drop my axes here. Um, and the
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way I'm gonna set up my bins is I'm gonna
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have them left endpoint. Inclusive. So this is
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gonna be zero. And if this is for the
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bar that's here, will include zero, but not
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Excuse me. I'll have this to be five.
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So the bar here will include zero, but not
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five. And that's what we want, cause the
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next barbell include five. So if we do that
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, I will have my been set up like this
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. 05 10 15 20 25 and 30. Um
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, and I'll choose to scale my ex excess up
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. Teoh. Let's just go by twos. Up
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to seven. So, too for six. Heat
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10 12 14. Time in 14 not seven.
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All right. And so now we can start drawing
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this out. So in our first been or 04
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we head nine. So that will be 2468 and
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up to nine right there in our second Been.
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We also had nines. That'll be right here in
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our third. We had 14 is all the way
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to the top at 14 there, and our fourth
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really had one, then spike up to five and
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then back down to one. From here, we
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can draw our frequency. Polygon. This is just
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connecting the mid points of the tops of each bar
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. So it'll look something like this is hand drawn
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. There's not gonna be perfect, but we'll have
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a curve that looks like this will give us a
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give us a shape. Um, that sort of
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described the shape of how, uh, these numbers
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are distributed. Now, the next thing he wants
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us to do is find, um the mean I
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was just find the mean What we do to find
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the mean we know is we sum up all of
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our data all of our exes, and defied by
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the number When I was a calculator to count everything
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up, I'm gonna get that. We have 300
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80. Uh, that the sum is 380.
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Um, and we know that we have 39 data
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points just from counting. So dividing one by the
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other will get that the mean. The exact meat
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is nine point 74 Now, the problem wants us
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to use the frequency table that we just made to
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find the mean We know that frequent finding the meat
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from frequency table we have export is equal to the
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sum of X times the frequency over some of the
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frequencies or end. We ready? Know that And
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is 39 doesn't really matter. But we need what
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is gonna be X Here we have our values,
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our ranges. So when our values air ranges,
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that means we need to take the mid points.
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Um, so our midpoint, they're gonna be as
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follows. We have midpoint to then seven, then
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12 17 and so on up until 27 and all
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right, down our frequencies again. So these are
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exes. Our frequencies are 99 14 15 and one
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. Now we can make a column. Another column
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is gonna be X times F and X times f
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is gonna look like this. 18 63 168 17
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10. And you're not 10 110 and 27.
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So now that we have X times, African adult
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is up and I have done this in the calculator
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. Another x times F Some of these is gonna
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equal 403. So x bar is going to be
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403 divided by 39 which is equal to uh,
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let's see. That's gonna be good to 10.33 Now
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what happened here? How is this different? We
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see we have an exportable tonight, boys. And
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Ford, an expert with a 10.33 next question,
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wants us to know how. How are these reconcilable
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? How can we have two different average is Well
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, what happens is this average found from the frequency
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table is just an estimate. It's an estimate because
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we took a bunch of values in our been.
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So we had several value nine values in our 0
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to 4 range. They're all over and we said
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, Let's just pretend that they're all too So we
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changed the data a little bit by making them all
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uniform. And that's how our answered changes just a
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little bit. Now, finally, this question wants
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us to answer which the median and what is the
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mode? Will the median we know we have an
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equal to 39 and so when we have an odd
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number of data, points are median is the point
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at 39 plus 1/2, which is 40 over to
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which is 20 our 20th data point sorted from least
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the highest or highest released. Um, and then
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we count that out. We'll find that our median
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is actually 10. And finally the mode, the
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mode, we know it's not very obvious. But
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when recounting it out, we see that we have
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five instances of 11 and ah, no other value
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shows of that many times, so our mode is
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equal to 11.